It is a contraction of 書いた の ですか, where 書いた is past tense of 書く (no iru in there). ーの です is a common ending form of a sentence to make it sound smoother. It does not change the meaning any way - you may think of it as "It is that ...." in English. And -の です is usually shortened to -ん です。(you see this form all over the place) か at the end is the suffix to turn it into a question. So, it becomes 書いたんですか, to mean "(Did you) write it?".

It's a good question!!! And really hard to explain lol "Ita" is the past tense of "Iru". "Kaita" is the past tense of "Kaku". I think you've already known these. And "書いたんですか" or "書いちゃったんですか" sounds like "Are you FREAKIN serious!?!? You really wrote!?!? You were not supposed to!!!"